论文标题
在一个轻度功能的家族中
On a family of mild functions
论文作者
论文摘要
我们证明$p_α（x）= \ exp（1-x^{ - α}）$，$α> 0 $，为$ 1/α$ -Mild。我们将此结果应用于曲线家族的均匀$ 1/α$ -Mild参数化，$ \ {xy =ε^2 \ mid（x，y）\ in（0,1）^2 \} $（0,1）$ in（0,1）$，这不是均匀的$ -Mild parametrization y y yommdin of yommdin of yommdin。更一般而言，我们可以参数能力划分曲线的家族。这改善了Benjamini和Novikov的结果，它给出了$ 2 $ MILD参数化的结果。
We prove that the function $P_α(x) = \exp(1-x^{-α})$ with $α> 0$, is $1/α$-mild. We apply this result to obtain a uniform $1/α$-mild parametrization of the family of curves $\{xy = ε^2 \mid (x,y) \in (0,1)^2\}$ for $ε\in (0,1)$, which does not have a uniform $0$-mild parametrization by work of Yomdin. More generally we can parametrize families of power-subanalytic curves. This improves a result of Benjamini and Novikov that gives a $2$-mild parametrization.
